SciPost Physics

SciPost Phys. 6, 057 (2019) · published 10 May 2019

• doi: 10.21468/SciPostPhys.6.5.057
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying magnetic fields. For free systems these fall into several universality classes, the most generic one being governed by the Tracy-Widom distribution. We investigate in this paper the effect of interactions. Using semiclassical arguments, we show that since the density vanishes to leading order, the strong interactions in the bulk are renormalized to zero at the edge, which simply explains the survival of Tracy-Widom scaling in general. For integrable systems, it is possible to push this argument further, and determine exactly the remaining length scale which controls the variance of the edge distribution. This analytical prediction is checked numerically, with excellent agreement. We also study numerically the edge scaling at fronts generated by quantum quenches, which provide new universality classes awaiting theoretical explanation.

• Stéphan, Exact time evolution formulae in the XXZ spin chain with domain wall initial state
  J. Phys. A: Math. Theor. 55, 204003 (2022) [Crossref]
• Riddell et al., Scaling at the out-of-time-ordered correlator wavefront: Free versus chaotic models
  Phys. Rev. B 108, L121108 (2023) [Crossref]
• Walsh, Interface fluctuations associated with split Fermi seas
  J. Phys. A: Math. Theor. 57, 085201 (2024) [Crossref]
• Pallister et al., Limit shape phase transitions: a merger of arctic circles
  J. Phys. A: Math. Theor. 55, 304001 (2022) [Crossref]
• Cafasso et al., Fredholm Determinant Solutions of the Painlevé II Hierarchy and Gap Probabilities of Determinantal Point Processes
  2021, 2437 (2021) [Crossref]
• Alba et al., Quantum information scrambling after a quantum quench
  Phys. Rev. B 100, 115150 (2019) [Crossref]
• Stéphan, Extreme boundary conditions and random tilings
  SciPost Phys. Lect. Notes, 26 (2021) [Crossref]
• Moriya et al., Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition
  J. Stat. Mech. 2019, 063105 (2019) [Crossref]
• Scopa et al., Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
  SciPost Phys. 12, 207 (2022) [Crossref]
• Bulchandani, Kardar-Parisi-Zhang universality from soft gauge modes
  Phys. Rev. B 101, 041411 (2020) [Crossref]
• Kulkarni et al., Density profile of noninteracting fermions in a rotating two-dimensional trap at finite temperature
  Phys. Rev. A 107, 023302 (2023) [Crossref]
• Riggio et al., Gradient corrections to the local-density approximation in the one-dimensional Bose gas
  Phys. Rev. A 106, 053309 (2022) [Crossref]
• Saenz et al.,
  289, 9 (2022) [Crossref]
• McRoberts et al., Domain Wall Dynamics in Classical Spin Chains: Free Propagation, Subdiffusive Spreading, and Soliton Emission
  Phys. Rev. Lett. 132, 057202 (2024) [Crossref]
• Bastianello et al., Entanglement entropies of inhomogeneous Luttinger liquids
  J. Phys. A: Math. Theor. 53, 155001 (2020) [Crossref]
• Bocini et al., Non-probabilistic fermionic limit shapes
  J. Stat. Mech. 2021, 013204 (2021) [Crossref]
• Krajenbrink, From Painlevé to Zakharov–Shabat and beyond: Fredholm determinants and integro-differential hierarchies
  J. Phys. A: Math. Theor. 54, 035001 (2021) [Crossref]
• Bulchandani et al., Superdiffusion in spin chains
  J. Stat. Mech. 2021, 084001 (2021) [Crossref]
• Modak et al., Entanglement revivals as a probe of scrambling in finite quantum systems
  J. Stat. Mech. 2020, 083110 (2020) [Crossref]
• Bhandari et al., Long time dynamics of a single-particle extended quantum walk on a one-dimensional lattice with complex hoppings: a generalized hydrodynamic description
  Quantum Inf Process 22, 43 (2023) [Crossref]
• Eisler et al., Front dynamics in the XY chain after local excitations
  SciPost Phys. 8, 037 (2020) [Crossref]
• Majumdar et al., Extreme value statistics of correlated random variables: A pedagogical review
  Physics Reports 840, 1 (2020) [Crossref]
• Buijsman et al., Ground-state energy distribution of disordered many-body quantum systems
  Phys. Rev. E 106, 054144 (2022) [Crossref]
• Betea et al., Multicritical Schur Measures and Higher-Order Analogues of the Tracy–Widom Distribution
  Math Phys Anal Geom 27, 2 (2024) [Crossref]
• De Bruyne et al., Wigner function for noninteracting fermions in hard-wall potentials
  Phys. Rev. A 104, 013314 (2021) [Crossref]
• Smith et al., Full counting statistics for interacting trapped fermions
  SciPost Phys. 11, 110 (2021) [Crossref]
• Misguich et al., Domain wall problem in the quantum XXZ chain and semiclassical behavior close to the isotropic point
  SciPost Phys. 7, 025 (2019) [Crossref]
• Mays et al., Tracy-Widom Distributions for the Gaussian Orthogonal and Symplectic Ensembles Revisited: A Skew-Orthogonal Polynomials Approach
  J Stat Phys 182, 28 (2021) [Crossref]